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ddrg
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math_formulas

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int64
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2,896
\left(1 + y^4/9\right)^{\frac12}\cdot 9^{\frac12} = \left(9 + y^4\right)^{1/2}
38,105
1 - 34/50*34/50 = \frac{1344}{2500}
-5,340
4.2 \cdot 10^{3 \cdot (-1) + 4} = 4.2 \cdot 10^1
8,225
\left(\left(-1\right) H_n\right)/(B_n*(-1)) = H_n/(B_n)
-18,799
x = \frac{x\cdot 9}{9}
12,223
h\cdot 36 + 4/h = 72 \implies 1 + h \cdot h\cdot 9 = 18\cdot h
19,068
\sec(x) = -25/7 \Rightarrow -\dfrac{7}{25} = \cos(x)
20,242
13 = (3 + 2\cdot \text{i})\cdot \left(3 - \text{i}\cdot 2\right)
12,172
-\cos(x) + \sin(x\cdot 0) = -\cos(x)
-1,964
π \cdot \frac{19}{12} + π \cdot 7/6 = \frac{1}{4} \cdot 11 \cdot π
25,570
\tanh(1) = \frac{e^2 + (-1)}{e e + 1}
-1,884
-7/4 \pi + 3/2 \pi = -\tfrac{\pi}{4}
1,283
\dfrac{1/13*6}{4}*4 = \dfrac{6}{13}
19,372
\left(\alpha \cdot \beta\right)^1 = \beta \cdot \alpha
23,645
\frac{1}{m!} \times (m + 1)! = m + 1
13,386
(-b + a)^2 = (-a + b) \cdot (-a + b)
22,802
\sqrt{8^2 + 4 \cdot 4 + (-8)^2} = 12
45,805
2 \cdot 3=6
27,567
c\cdot \overline{z} = \overline{z\cdot \overline{c}}
-3,803
4 \cdot t \cdot t \cdot t = t^3 \cdot 4
-4,413
(2\cdot (-1) + z)\cdot (4\cdot (-1) + z) = z^2 - 6\cdot z + 8
-20,249
\dfrac{1}{-4 \cdot y + 9} \cdot (-4 \cdot y + 9) \cdot 9/2 = \dfrac{81 - 36 \cdot y}{18 - 8 \cdot y}
1,098
B \times B + A^2 + B \times A \times 2 = B^2 + A^2 + A \times B + B \times A
19,393
(2 - 1/3)\cdot \left(3 - 1/5\right)\cdot (-1/2 + 5) = 21
16,828
g \times E = g \times E
2,186
s = s \cdot s = (-s)^2 = -s
7,192
x^{10} = \left(1 - x\right)\times (13 - 21\times x) = 21\times x \times x - 34\times x + 13 = 21\times (1 - x) - 34\times x + 13 = 34 - 55\times x
26,537
-(3*\sqrt{3} + 5)/2 = -\frac{5}{2} - \sqrt{3}*3/2
12,189
\left(-5\right)^2 + \left(-3\right)^2 + 1^2 = 35 = 5*(\left(-5\right)*(-3) - 5 - 3)
7,743
d/dy (4 + y^3 + y^2*2 + 3*y) = 3 + 3*y^2 + y*4
-9,200
-k \cdot 72 + 36 \cdot \left(-1\right) = -k \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 - 2 \cdot 2 \cdot 3 \cdot 3
-25,871
y^3 = \frac{y^5}{y^2}
30,264
b + c \neq 0 \Rightarrow b \neq -c
38,347
\left(k_2 + 1\right)! + (-1) = \left(k_2 + 1\right)\cdot k_2! + (-1) = (k_1 + 1)\cdot k_2! + (k_2 - k_1)\cdot k_2! + (-1) > (k_1 + 1)\cdot k_2!
14,975
x\cdot x + 2\cdot x\cdot d + d\cdot d = (d + x)\cdot \left(x + d\right)
2,856
\frac{1}{Y}Z^Q = \frac{1}{Y}Z^Q
-21,610
\sin(\frac12\pi) = 1
-3,109
\sqrt{25\cdot 3} + \sqrt{16\cdot 3} = \sqrt{48} + \sqrt{75}
-11,540
4 + 6\cdot i = 6\cdot i + 4 + 0\cdot \left(-1\right)
-29,320
-4 + 8 + i\cdot 18 = 4 + 18\cdot i
1,999
{(-1) + x + r \choose x} = {(-1) + x + r \choose r + (-1)}
15,244
1 + \frac{2}{b + (-1)} = \frac{1 + b}{(-1) + b}
29,779
\frac{4}{6^3}\cdot 6\cdot 5 = 5/9
-1,898
-\frac{\pi}{6} = -13/12 \pi + \pi \tfrac{11}{12}
26,421
-\frac{1}{x\cdot (1 - 1/x)} = \frac{1}{-x + 1}
-9,458
t \cdot 60 + 54 = t \cdot 2 \cdot 2 \cdot 3 \cdot 5 + 2 \cdot 3 \cdot 3 \cdot 3
2,442
o^6 + y^6 = (o^2)^3 + (y^2)^3 = \left(o \cdot o + y^2\right) \cdot \left(o^4 - o^2 \cdot y^2 + y^4\right)
1,501
1 + b + b^2 + b^3 + \ldots + b^x = \frac{1}{1 - b}\cdot (-b^{x + 1} + 1)
-9,397
-3 \times 2 \times 2 \times 2 \times 2 + x \times 2 \times 3 \times 3 = 18 \times x + 48 \times (-1)
-4,715
\dfrac{7 \times x + 15}{x^2 + x \times 6 + 5} = \dfrac{2}{x + 1} + \frac{5}{x + 5}
17,756
\sqrt{2} = 1.414213562373*...
24,796
1/(L\cdot U) = \frac{1}{L\cdot U}
8,901
(0^2 + 1 \cdot 1)^2 + 2^2 = \left(0 + 1\right)^2 + 2 \cdot 2 = 1^2 + 2^2 = 1 + 4 = 5
-20,772
\dfrac{-8\cdot n + 24}{15\cdot (-1) + n\cdot 5} = \dfrac{n + 3\cdot (-1)}{3\cdot \left(-1\right) + n}\cdot (-\frac15\cdot 8)
15,319
\sin^l{x} = \sin^{l + 2*(-1)}{x}*\sin^2{x} = \sin^{l + 2*(-1)}{x}*\left(1 - \cos^2{x}\right)
26,924
\left(-1\right) + 10*4 = 39
-7,519
19/3 = \frac1957
14,728
|2\cdot e^{i\cdot t} + (-1)|^2 = |2\cdot \cos{t} + 2\cdot i\cdot \sin{t} + (-1)|^2 = \left(2\cdot \cos{t} + (-1)\right)^2 + (2\cdot \sin{t})^2
11,998
\dfrac{1}{\sqrt{r + 3 (-1)}} = \sqrt{\frac{1}{r + 3 \left(-1\right)}} = \sqrt{e^{3 r}}
42,110
d^0 d^1 = d^1 = d^1
20,115
d^{i + 1}\cdot x^{i + 1} = d\cdot x\cdot (d\cdot x)^i = d\cdot x\cdot d^i\cdot x^i
32,199
\dfrac{1}{455} \cdot 64 = 384/2730
23,745
|x + b|^2 = (x + b)*\overline{x + b} = \left(x + b\right)*(\overline{x} + \overline{b})
-20,342
3/3 \cdot \frac{1}{-3 \cdot k + 3 \cdot (-1)} \cdot (\left(-2\right) \cdot k) = \frac{1}{-9 \cdot k + 9 \cdot (-1)} \cdot (k \cdot \left(-6\right))
-18,962
\frac{1}{3} = \frac{B_s}{25\cdot \pi}\cdot 25\cdot \pi = B_s
4,792
(-1) + \frac{k}{u + k} = \frac{u \cdot (-1)}{u + k}
32,883
x^6 x^n = x^{6 + n}
-7,031
\frac{5}{13}\cdot 6/14 = 15/91
-30,582
-\left(2\cdot x + 3\right)\cdot 7 = -x\cdot 14 + 21\cdot (-1)
1,836
E_x \cdot E_l = E_l \cdot E_x
-1,485
-2/9 (-9/5) = \frac{1}{1/2 (-9)}((-1) \cdot 9 \cdot \frac15)
4,850
\left(36/100 = 4/z \Rightarrow z \cdot 36 = 400\right) \Rightarrow 11.11 = z
50,482
3 + 1108 = 1111
17,981
1 - (\tfrac56)^6 = 31031/46656
10,830
x = \dfrac{1}{1^{-1}}\cdot x = x/1 = x
-162
\binom{9}{3} = \frac{9!}{\left(3 \cdot (-1) + 9\right)! \cdot 3!}
-1,505
7\cdot \frac{1}{8}/(8\cdot 1/7) = 7/8\cdot 7/8
-18,604
z = 5 \cdot (5 \cdot z + 6 \cdot (-1)) = 25 \cdot z + 30 \cdot (-1)
20,717
p^{m + 1} \gt p^{m + 1} + (-1) = (p^m + (-1))^p > p^{\left(m + (-1)\right)*p}
21,468
p^2 + p*2 + 9 = 8 + \left(1 + p\right)^2
-6,562
\frac{1}{4\cdot l + 28\cdot (-1)}\cdot 4 = \frac{4}{(l + 7\cdot (-1))\cdot 4}
6,539
x + 1 + 2*(-1) = x + (-1)
13,812
\sin{\theta} = \frac{2\cdot \tan{\theta/2}}{\tan^2{\frac12\cdot \theta} + 1}
-22,235
(k + 6)\cdot (k + 9) = 54 + k^2 + 15\cdot k
-17,406
\dfrac{127.6}{100} = 1.276
-1,289
-9/5\cdot 6/1 = ((-9)\cdot \frac15)/(\tfrac16)
-1,252
-\frac57\cdot 7/1 = (\frac17 (-5))/(\frac17)
37,940
{5 \choose 4}*{8 \choose 4} = 350
14,793
x^3 + (-1) = (x + (-1)) \cdot \left(1 + x \cdot x + x\right)
15,491
|x*D| = |x*D|
14,967
D^T D = D^T D
-17,477
7 = 32 + 25 \left(-1\right)
-5,210
10^5\cdot 7.1 = 7.1\cdot 10^{(-4) (-1) + 1}
6,727
\frac{2}{7!}\cdot 6! = \frac{2}{7}
-20,439
\frac{1}{8*j + 16}*(7*j + 14) = 7/8*\frac{1}{j + 2}*(2 + j)
9,208
564.453 \lt 1000 \vartheta \lt 564.484 \Rightarrow 564 = \left\lfloor{1000 \vartheta}\right\rfloor
-8,077
\left(38 - 8i + 95 i + 20\right)/29 = \frac{1}{29}(58 + 87 i) = 2 + 3i
-18,955
3/5 = x_r/(25*\pi)*25*\pi = x_r
-11,971
\tfrac{71}{90} = p/(12*\pi)*12*\pi = p
-10,663
12/12*\frac{1}{c^2}*2 = \frac{1}{12*c * c}*24